Sister Beiter conjecture

In mathematics, the Sister Beiter conjecture is a conjecture about the size of coefficients of ternary cyclotomic polynomials (i.e. where the index is the product of three prime numbers). It is named after Marion Beiter, a Catholic nun who first proposed it in 1968.

Background
For $$n\in\mathbb{N}_{>0}$$ the maximal coefficient (in absolute value) of the cyclotomic polynomial $$\Phi_n(x)$$ is denoted by $$A(n)$$.

Let $$3\leq p\leq q\leq r$$ be three prime numbers. In this case the cyclotomic polynomial $$\Phi_{pqr}(x)$$ is called ternary. In 1895, A. S. Bang proved that $$A(pqr)\leq p-1$$. This implies the existence of $$M(p):=\max\limits_{p\leq q\leq r\text{ prime}}A(pqr)$$ such that $$1\leq M(p)\leq p-1$$.

Statement
Sister Beiter conjectured in 1968 that $$M(p)\leq \frac{p+1}{2}$$. This was later disproved, but a corrected Sister Beiter conjecture was put forward as $$M(p)\leq \frac{2}{3}p$$.

Status
A preprint from 2023 explains the history in detail and claims to prove this corrected conjecture. Explicitly it claims to prove $$ M(p)\leq\frac{2}{3}p \text{ and } \lim\limits_{p\rightarrow\infty}\frac{M(p)}{p}= \frac{2}{3}. $$